If you run out of lives, you can turn off the game and turn it back on, or hit return to title screen, either way go to continue and you will get to load you're auto save data and won't have to start at the begining of the level.
When you beat Normal Mode, Hard Mode (with different bosses, weapons, stages, and capsules) will be unlocked.
Beat Hard Mode to unlock Xtreme Mode.
Xtreme Mode does away with just about all story elements, but combines all the bosses, weapons, capsules, etc. from Normal and Hard Mode.